For computing D-dimensional helicity amplitudes, especially for amplitudes at the loop level,
one typically uses the projection method [1]}, [2]}, [3]}
which is based on Lorentz covariant tensor decomposition of scattering amplitudes (with external state vectors being stripped off).
The entire dependence of loop amplitudes on loop integrals is encoded in the Lorentz invariant
decomposition coefficients which multiply the relevant Lorentz tensor structures.
Lorentz tensor decomposition is employed, for instance, at one loop in the
Passarino-Veltman reduction procedure [4]}, and also in
the systematic constructions of dimensionally regularized QCD helicity amplitudes [5]}, [6]}.
During the last decades, there have been many computations done for high order QCD corrections to scattering amplitudes using the projection method, for example, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}, [24]}, [25]}, [26]}, [27]}, [28]}, [29]}, [30]}, [31]}, [32]}, [33]}, [34]}, [35]}, [36]}, [37]}, [38]}, [39]}, [40]}.
